Embedding of the classical into the quantum description of photons

Abstract

The macroscopic properties of a many-particle quantum system are revealed by an embedding of the macroscopic classical into the microscopic quantum description of the system. Such an embedding is based on the assumption that the experiments to which the classical theory applies may also be described quantum mechanically. It results from the existence of an injective trajectory observable. For photon quantum systems with a finite number of modes an embedding is explicitly constructed using the well- known phase space observable for quantum systems of finite degrees of freedom. For the general case of photon quantum fields the existence of a phase space observable is shown which, restricted to a finite number of modes, coincides with the mentioned one.